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Homework Assignment 2:
(1) For a certain type of policy an insurance company divides its claims into two classes, minor and
major. Last year 90% of the policyholders filed no claims, 9 percent filed minor claims and 1
percent filed major claims.
The amounts of the minor claims were uniformly distributed over
(0,1000), and the major claims were uniformly distributed over (1000,10000).
Let X = the amount
paid to a randomly selected policyholder.
Find F(x) for 0
≤
x
≤
10000.
Ans:
F(0) = .90
F(x) = .90 + .09x/1000 for 0 < x
≤
1000
F(x) = .99 + .01(x – 1000)/9000 for 1000 < x
≤
10000
(2) A random loss has the following probability distribution:
Amount of Loss:
0
1
2
3
5
6
7
9
Probability
: .5
.1
.1
.1
.1
.05
.025
.025
An insurer will pay nothing if the loss is
≤
2, and will pay the loss minus 2 if the loss is > 2, but the
maximum payment will be 4.
Find the variance of the payment.
(Ans 1.96)
(3) An insurance policy reimburses a loss up to a benefit limit of 10.
The policyholder’s
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 Spring '11
 CharlesDann

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